A lot of violet LED output is in UV, not visible violet. Also, you are WAY less sensitive to violet light than you are to green light. An equivalent apparent brightness of green vs. violet LED requires a violet LED that is actually far brighter than the sun in the sky, just not all visible.

Another thing to remember is that that white LED probably has a big output in UV frequencies, too.

Anyways, the dangerousness of the light is going to be related, generally, to the energy each photon carries. This can be calculated using Planck's constant (h) and the speed of light (c). {I need to use some unicode characters, I guess, to get lambda and Planck's constant.} As the wavelength decreases, from UV to further UV to X-rays, the energy carried by each photon increases.

energy = h * c / wavelength

It is the higher energy, shorter wavelengths radiation that will make a Mars mission dangerous.

I was considering this recently too. You can get these water purifiers that use UV light now, but I don't see anywhere where it says to not look at it when you're using it... UV burns, Kalkin. I know you're not supposed to look at the light of a chip wiper, and that's UV.

UV air purifiers (which have been around for ages, actually) use mercury vapor lamps emitting at ~250 nm in the UVC range, which is not good for you.

a 405 nm LED probably has several nm of bandwidth around 405, maybe extending a little into the UVA range, but should be mostly safe. The main danger with violet and deep-red is that you can see them, but they are much brighter than they appear, which makes eye damage more likely. They also don't trigger the iris closing reflex well, so your eye lets more light in. This is a serious problem with lasers, much less so with LEDs--few LEDs can get bright enough to cause eye damage. I wouldn't hold it up next to my eye and stare into the LED, but other than that, don't worry too much about it.

White LEDs may have a fair amount of UV emission, however, it will be diffused, making it even less dangerous.